Accelerated Stochastic Zeroth-Order Quasar-Convex Optimization
Abstract
We consider unconstrained minimization of smooth quasar-convex functions when only noisy function evaluations are accessible through a stochastic zeroth-order oracle. For these non-convex functions, the standard acceleration method relies on subspace-search mechanisms that require first-order information, being therefore unavailable in zeroth-order regimes. In contrast, the alternative and less conventional continuized method enable to avoid such mechanisms. In this work, we design a zeroth-order continuized algorithm, leading to accelerated convergence guarantees that parallel those of smooth convex optimization up to a quasar-convexity parameter. Our method incorporates a mirror step, improving the dimension dependence when there exists sparse solution.
Related
- Adaptive two-points zero-order accelerated methods for stochastic convex optimization problems
- Near-Optimal Exact-Value Zeroth-Order Complexity for Smooth Strongly Convex Optimization
- Sharp Minimax Rates for Highly Smooth Strongly Convex Zeroth-Order Optimization
- Weakly Quasar-Convex Optimization
- Stochastic Lie-Bracket Approximations for Zeroth-Order Optimization on Manifolds
BibTeX
@misc{gbaguidi2026accelerated,
title = {{Accelerated Stochastic Zeroth-Order Quasar-Convex Optimization}},
author = {Eméric Gbaguidi and Julien Hermant},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05753170v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Accelerated Stochastic Zeroth-Order Quasar-Convex Optimization
AU - Eméric Gbaguidi
AU - Julien Hermant
PY - 2026
DA - 2026/09/17
PB - HAL
UR - https://hal.science/hal-05753170v1
AB - We consider unconstrained minimization of smooth quasar-convex functions when only noisy function evaluations are accessible through a stochastic zeroth-order oracle. For these non-convex functions, the standard acceleration method relies on subspace-search mechanisms that require first-order information, being therefore unavailable in zeroth-order regimes. In contrast, the alternative and less conventional continuized method enable to avoid such mechanisms. In this work, we design a zeroth-order continuized algorithm, leading to accelerated convergence guarantees that parallel those of smooth convex optimization up to a quasar-convexity parameter. Our method incorporates a mirror step, improving the dimension dependence when there exists sparse solution.
ER -